Question
Find the remainder when 345 is divided by 10.
Solution
ATQ, Powers of 3 mod 10 repeat every 4: 31→3, 32→9, 33→7, 34→1 (cycle length 4) 45 ÷ 4 gives remainder 1 (since 45 = 4×11 + 1) So remainder = 31 mod 10 = 3
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